Unfortunately, this all comes down to a decision by the modder (taken by several modders) to not support singleplayer. Some do this out of a belief that ‘singleplayer isn’t a proper game mode’, more often it is simply that they themselves only play on servers and they don’t want to put in the extra work and time in testing for a mode they have no interest in. It is unfortunate for us, but they have that right - they put in the work constructing their mods because they want to, and they have no obligation to make them available to any game mode that they do not wish to support.
Dedicated server is, as you know, an alternative way around this issue, but can (as you have discovered) have problems of its own. I would suggest seeking advice in this thread as it is maintained and regularly answered by the guy who created the dedicated server tool for the game. It sounds like you already know what the problem is and that there may be no solution, but if anyone would have an idea that might help, that would be the place to find it.
It is unfortunate, but there are simply some mods that we as singleplayers do not get to have access to (or at least not reliable performance) - that is the choice of the modders that make them, and we have to live with that. I hope you are able to find some way to get a dedicated server working as that is reportedly the best solution. But otherwise, you may just have to accept that Tot mods are not available for us.